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how do i solve 2^x=7?

 Apr 18, 2014

Best Answer 

 #2
avatar+102948 
+5

how do i solve 2^x=7?

Let me give you an example.....then you should be able to do this one....

Suppose we had   4x = 9

First....take the "log" of both sides......this gives us

log 4x = log 9

By a property of logarithms, we can bring the "x" in front of the "log 4"......and we have

x log 4 = log 9......now, divide both sides by the "log 4" .....and we have

x = log 9 / log 4........ we can evaluate this on the calculator on this site, and we find that

x ≈ 1.58

 

Be careful !!!   Some students - mistakenly - take the log of (9/4).....this is NOT the same thing as

log 9 / log 4     

I think you have enough to get you on the right road, now.........

 Apr 19, 2014
 #1
avatar+890 
+5

Take logs (any base) and then use the rule

 $$\log (a^{n})=n\log(a)$$.

 Apr 18, 2014
 #2
avatar+102948 
+5
Best Answer

how do i solve 2^x=7?

Let me give you an example.....then you should be able to do this one....

Suppose we had   4x = 9

First....take the "log" of both sides......this gives us

log 4x = log 9

By a property of logarithms, we can bring the "x" in front of the "log 4"......and we have

x log 4 = log 9......now, divide both sides by the "log 4" .....and we have

x = log 9 / log 4........ we can evaluate this on the calculator on this site, and we find that

x ≈ 1.58

 

Be careful !!!   Some students - mistakenly - take the log of (9/4).....this is NOT the same thing as

log 9 / log 4     

I think you have enough to get you on the right road, now.........

CPhill Apr 19, 2014
 #3
avatar+103674 
+3

Whenever the unknown is an exponent (a power for Australians)  you can solve the equation by taking the log of both sides.  

It doesn't matter what base you use but calculators only dealy with base 10 and base e.

 Apr 19, 2014

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